Question 827274
Set L = the length of the longer side
{{{2/3 = W/L}}}
do cross products
 {{{3W = 2L}}}
divide each side by 3
{{{W = (2/3)L}}}

Since L * W = Area
      L * W = 150
Substituting (2/3)L for W
      {{{( L*(2/3)L ) = 150}}}
multiply each side by 3/2
     {{{( L*L ) = 150(3/2)}}}
{{{( L^2 ) = 450/2}}}
{{{( L^2 ) = 225}}}
{{{L = 15}}}
Since {{{W = (2/3)L}}} , W = 10